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Impact Factor:1.318
Affiliation of Author(s):Shool of Mathematical sciencs,
Journal:TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Place of Publication:201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA
Funded by:National Natural Science Foundation of China (Grant No. 11271283)
Key Words:Jacobi forms, arithmetic of quaternion algebras
Abstract:We use the theory of Jacobi forms to study the number of elements in a maximal order of a definite quaternion algebra over the field of rational numbers whose characteristic polynomial equals a given polynomial. A certain weighted average of such numbers equals (up to some trivial factors) the Hurwitz class number H(4n−r2). As a consequence we obtain new proofs for Eichler’s trace formula and for formulas for the class and type number of definite quaternion algebras. As a secondary result we derive explicit formulas for Jacobi Eisenstein series of weight 2 on Γ0(N) and for the action of Hecke operators on Jacobi theta series associated to maximal orders of definite quaternion algebras.
Co-author:Haigang Zhou
Indexed by:Article
Volume:371
Issue:9
Page Number:6487-6509
ISSN No.:0002-9947
Translation or Not:no
Date of Publication:2019-01-01
Included Journals:SCOPUS、CNKI、WOS